Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 186 · 40 questions

How to solve it (Across, up, Pythagoras): Distance: across = difference of the x values, up = difference of the y values; distance = √(across² + up²). Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Quadrants by signs: (+, +) first, (−, +) second, (−, −) third, (+, −) fourth.

1. 1.What is the midpoint of the line joining (6, 13) and (18, 5)? (a) (6, 4) (b) (24, 18) (c) (12, 9) (d) (9, 12)
2. 2.In which quadrant does the point (−1, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
3. 3.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
4. 4.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
5. 5.What is the distance between the points (3, 5) and (18, 13)? (a) 17 (b) 289 (c) 18 (d) 23
6. 6.What is the midpoint of the line joining (9, 9) and (11, 1)? (a) (10, 5) (b) (1, 4) (c) (5, 10) (d) (20, 10)
7. 7.What is the distance between the points (1, 11) and (13, 6)? (a) 13 (b) 17 (c) 14 (d) 169
8. 8.What is the midpoint of the line joining (6, 16) and (12, 8)? (a) (9, 12) (b) (12, 9) (c) (18, 24) (d) (3, 4)
9. 9.In which quadrant does the point (3, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
10. 10.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
12. 12.In which quadrant does the point (−9, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
13. 13.In which quadrant does the point (1, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
14. 14.What is the midpoint of the line joining (8, 13) and (20, 7)? (a) (28, 20) (b) (6, 3) (c) (14, 10) (d) (10, 14)
15. 15.What is the midpoint of the line joining (8, 4) and (12, 2)? (a) (2, 1) (b) (20, 6) (c) (3, 10) (d) (10, 3)
16. 16.What is the distance between the points (1, 0) and (13, 5)? (a) 17 (b) 169 (c) 14 (d) 13
17. 17.What is the midpoint of the line joining (0, 6) and (12, 10)? (a) (12, 16) (b) (6, 8) (c) (6, 2) (d) (8, 6)
18. 18.In which quadrant does the point (−7, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
19. 19.What is the midpoint of the line joining (1, 2) and (9, 6)? (a) (10, 8) (b) (5, 4) (c) (4, 5) (d) (4, 2)
20. 20.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
21. 21.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
22. 22.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
23. 23.What is the distance between the points (9, 4) and (15, 12)? (a) 11 (b) 10 (c) 14 (d) 100
24. 24.In which quadrant does the point (−5, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
25. 25.In which quadrant does the point (1, 3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
26. 26.In which quadrant does the point (−5, −9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
27. 27.In which quadrant does the point (−5, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
28. 28.What is the midpoint of the line joining (6, 0) and (10, 4)? (a) (16, 4) (b) (2, 2) (c) (2, 8) (d) (8, 2)
29. 29.In which quadrant does the point (1, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
30. 30.What is the midpoint of the line joining (7, 10) and (9, 2)? (a) (6, 8) (b) (16, 12) (c) (8, 6) (d) (1, 4)
31. 31.In which quadrant does the point (7, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
32. 32.What is the midpoint of the line joining (10, 13) and (20, 5)? (a) (15, 9) (b) (5, 4) (c) (30, 18) (d) (9, 15)
33. 33.What is the distance between the points (6, 2) and (18, 11)? (a) 16 (b) 15 (c) 21 (d) 225
34. 34.What is the distance between the points (7, 0) and (14, 24)? (a) 31 (b) 625 (c) 25 (d) 26
35. 35.What is the midpoint of the line joining (1, 10) and (11, 16)? (a) (12, 26) (b) (6, 13) (c) (5, 3) (d) (13, 6)
36. 36.In which quadrant does the point (4, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
37. 37.What is the midpoint of the line joining (4, 11) and (8, 7)? (a) (9, 6) (b) (12, 18) (c) (6, 9) (d) (2, 2)
38. 38.What is the distance between the points (2, 13) and (17, 5)? (a) 23 (b) 17 (c) 289 (d) 18
39. 39.What is the distance between the points (9, 3) and (13, 6)? (a) 6 (b) 5 (c) 7 (d) 25
40. 40.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28

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